I've used/added the USPS API into a system and it took practically no time at all to do it. I'm guessing that is significantly less time than building an AI tool. What's worse is that the thing that takes the least time to implement actually provides good data.
Obviously adding the USPS API to your tool would take less time than building an AI tool. But the AI tool is infinitely more powerful for almost anything other than dealing with addresses.
So the question isn't which one you can add to your tool faster. The question is, if I already have this AI tool setup, is it worth setting up the USPS API to go from 95% accuracy to 99.9% accuracy. For countless applications, it wouldn't be. Obviously if you need to scale and need to ensure accuracy, it's a different story.
If having something like the zip code not be accurate, then what's the point of having the zip code in your data? People writing code to store zips/addresses are doing it to not not be able to send/verify/etc. They are doing so that the can, but if the data is wrong then they can't.
What countless applications that ask for a zip code/mailing address and don't need it to be accurate? I would then say that any that you name would actually not need the data in the first place. If your hoover it up just to sell later, wouldn't it be worth more to be valid? So again, I'm right back to why do you need it?